What is the measure of

[tex]2 \sec^2 x = 3- \tan x \\\\\implies 2(1 +\tan^2 x) = 3- \tan x \\\\\implies 2 + 2 \tan^2 x +\tan x -3 =0\\\\\implies 2 \tan^2 x + \tan x -1 =0\\\\\implies 2u^2 + u -1 =0~~~ ;[\text{set} \tan x = u]\\\\\implies u = \dfrac{-1\pm \sqrt{1-4\cdot 2 \cdot (-1)}}{2(2)}\\\\\implies u =\dfrac{-1 \pm\sqrt{9}}{4}\\\\\implies u = \dfrac{-1 \pm 3}{4}\\\\\implies u = \dfrac{2}{4}=\dfrac 12~~ \text{or} ~~u =\dfrac{-4}{4} =-1\\\\[/tex]

[tex]\implies \tan x = \dfrac 12 ~~ \text{or} ~~ \tan x =-1~~~ ;[\text{Substitute back u =tan x}]\\\\\text{Now,}~ \\\\\tan x = -1,\\\\\implies x = n\pi - \dfrac{\pi}4\\\\\\\text{For interval,}~ [0,2\pi) \\\\x = \dfrac{3\pi}4, \dfrac{7\pi}4\\\\\text{In degrees,}~ x = 135^{\circ}, x =315^{\circ}\\\\\tan x = \dfrac 12\\\\\implies x = n\pi + \tan^{-1} \left(\dfrac 12 \right)\\\\\text{For interval} ~[0,2\pi),\\\\[/tex]

[tex]x=\tan^{-1} \left(\dfrac 12 \right), \left[\pi +\tan^{-1} \left( \dfrac 12 \right)\right]\\\\\text{in degrees,} ~~x=\tan^{-1} \left(\dfrac 12 \right), \left[180^{\circ} +\tan^{-1} \left( \dfrac 12 \right)\right]\\\\\\\\\text{Combine all solutions:}\\\\x=\dfrac{3\pi}4, \dfrac{7\pi}4, \tan^{-1} \left(\dfrac 12 \right), \left[\pi +\tan^{-1} \left( \dfrac 12 \right)\right]\\\\\\[/tex]

[tex]\text{In degrees,}~ x = 135^{\circ},~315^{\circ},~\tan^{-1} \left(\dfrac 12 \right), \left[180^{\circ} +\tan^{-1} \left( \dfrac 12 \right)\right][/tex]

We must see which thing would make the conditional statement a false statement. We will see that the correct option is:

"You go to the gym for an hour a week and lose 7 pounds in a month"

So we start with the conditional statement:

"If you go to the gym for an hour a week, then you will lose at least 10 pounds in a month"

Remember that the general conditional statement is:

Where P is the hypothesis and Q is the conclusion.

The conditional statement is false if:

P is true and Q false.

So the given statement is only false if you meet the hypothesis (you go to the gym for an hour a week) but not the conclusion (you lose less than 10 pounds in a month).

With that in mind, the correct option is the third one, the only one where you lose less than 10 pounds in a month.

"You go to the gym for an hour a week and lose 7 pounds in a month"

If you want to learn more about conditional statements, you can read:

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Answer:

answer is attached on the photo

Answer:

768x4%= 30.72

His commission was $30.72

Step-by-step explanation:

Answer:

C:   H > 60

Step-by-step explanation:

H is 60 in or taller, underlined indicates that it's also 60 in, not just above it.

Answer:

Answer:

B

Step-by-step explanation:

3(x +1) =3x +3

Plug it in

3(5+1)=3(5)+3

3(6)=15+3

18=18

Answer:

Since the sides across from each other are congruent, you can times them by two

2(4x-6)+2(3x+4)

Answer:

P = 3.86n

Step-by-step explanation:

the price will be how many sets you buy multiplied by the price.

Answer:

You can either choose B or D.

Answer:

22 pounds and 13 ounces

Step-by-step explanation:

I hope this helps!

Answer:

36 seconds

Step-by-step explanation:

30 / (5 x 60) = 0.01

0.01 hours = 0.6 minutes

0.6 minutes = 36 seconds

Answer:

10 minutes

Step-by-step explanation:

First, we need to convert hours to minutes. 5 x 60 = 300.

300 minutes for 30 miles.

Next, divide both numbers by something to equal 1. (Divide it by 30, because we are trying to get 30 to 1.)

300 divided by 30 = 10

30 divided by 30 = 1

So, it would take Jack 10 minutes to ride 1 mile.

Answer:

  C = 18

Step-by-step explanation:

Put the numbers in place of their symbols and do the arithmetic. The diagram is showing you r = 3.

  C = 2πr

  C = 2(3)(3) . . . . . using 3 for π, as directed

  C = 18

[tex]\huge\bf\underline{\underline{\pink{A}\orange{N}\blue{S}\green{W}\red{E}\purple{R:-}}}[/tex]

Here we've been provided with the information given that radius (r) = 3.

And we have to find the circumference (c) of circle. And we have been provided with the formula i.e C = 2πr.

Placing (π = 3) in the above equation,

[tex]:\implies\tt{c = 2\pi r}[/tex]

[tex]:\implies\tt{c = 2 \times 3 \times 3}[/tex]

[tex]:\implies\tt{c = 6 \times 3}[/tex]

[tex]:\implies\tt{c = 18}[/tex]

[tex]\dfrac{10}{1+2i}\\\\\\=\dfrac{10(1-2i)}{(1+2i)(1-2i)}\\\\\\=\dfrac{10-20i}{1 - (2i)^2}\\\\\\=\dfrac{10-20i}{1+4}~~~~~;[i^2 =-1]\\\\\\=\dfrac{10-20i}5\\\\=\dfrac{10}5 - \dfrac{20i}5\\\\=2-4i[/tex]

Answer:

2,826

Step-by-step explanation:

A tenth is the first place value after the decimal point

In this case, 2,826.00

To round a number to the tenths place, we look at the hundredths place

If the number is 5 or more, we add 1 to the tenths place, and leave the numbers to the right 0's

If the number is 4 or less, we keep the number as it is in the tenths place, and leave the numbers to the right 0's

In this case, the hundredths place is a 0, which is less than 4, so we keep the 0 in the tenths place, and leave the to the right 0's.

Thus, our final answer is 2,826.

Answer:

A

Step-by-step explanation:

Benjie's line is a better fit because it has a lower value of least square residual, which measures how far on average each point is from the line.

Answer:

y = [tex]\frac{1}{2}[/tex] x - 4

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - 2x + 8 ← is in slope- intercept form

with slope m = - 2

Given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-2}[/tex] = [tex]\frac{1}{2}[/tex] , then

y = [tex]\frac{1}{2}[/tex] x + c ← is the partial equation

To find c substitute (6, - 1 ) into the partial equation

- 1 = 3 + c ⇒ c = - 1 - 3 = - 4

y = [tex]\frac{1}{2}[/tex] x - 4 ← equation of perpendicular line

Answer:

0.0005, 1/5/100, 5/1000, 5%, 50/100, 50, 500%

Step-by-step explanation:

You can convert all the percentages and fractions into decimals for better comprehension.

0.0005

1/5/100 = 0.002

5/1000 = 0.005

5% = 0.05

50/100 = 0.5

50

500% = 500

Answer:

0.0005, 1/5/100, 5/1000, 5%, 50/100, 50, 500%

Step-by-step explanation:

Answer:

x = ±[tex]\sqrt{7}[/tex] - 5

Step-by-step explanation:

x^2 - 10x = -18

x^2 - 10x + 18 = 0

(x + 5)^2 - 5^2 + 18 = 0

(x + 5)^2 - 7 = 0

(x + 5)^2  = 7

[tex]\sqrt{(x + 5)^2}[/tex] [tex]=[/tex] ±[tex]\sqrt{7}[/tex]

x = ±[tex]\sqrt{7}[/tex] - 5

Answer:

The answer is 1

Step-by-step explanation:

p² + p + 1; p = -1

Now, Put p = - 1

p² + p + 1

(-1)² + (-1) + 1

1 - 1 + 1 = 1

Thus, The answer is 1

-TheUnknownScientist 72

Hey there!

p(p^2 + p + 1)

= -1(-1^2 + (-1) + 1)

= -1(-1^2 - 2 + 1)

= -1(-1^2) - 1(-2) - 1(1)

= 1 + 2 - 1

= 3 - 1

= 2

Therefore, your answer should be: 2

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

Answer: 63

Step-by-step explanation:

[tex]a_4=-1+8^8\\a_4=63[/tex]

Answer:

Simplify x+1-2x+1−2 to x-1x−1.

x-1=4

x−1=4

2 Add 11 to both sides.

x=4+1

x=4+1

3 Simplify 4+14+1 to 55.

x=5

x=5

Add 11 to both sides.

x=2+1

x=2+1

2 Simplify 2+12+1 to 33.

x=3

x=3

Answer:

b= 1/3n - 8a/3

Step-by-step explanation:

hope that help you mark me brinilylist

Answer:

Sophia read 32 books and her brother read 8

Step-by-step explanation:

Represent Sophia as 4x and her brother as x

4x + x = 40

5x = 40

x = 8

Therefore, her brother read 8 books and Sophia read 32 books

Answer:

[tex]y=-\frac{1}{3}(x-2)^2+4[/tex]

Step-by-step explanation:

Vertex form of a parabola is [tex]y=a(x-h)^2+k[/tex] with the vertex being [tex](h,k)[/tex] and the vertical stretch or shrink factor as [tex]a[/tex].

Therefore, the correct equation is [tex]y=-\frac{1}{3}(x-2)^2+4[/tex]

The equation in vertex form of the downward-opening parabola with vertex (2, 4) that is stretched by a factor of 3.

The vertex form of a downward-opening parabola is given by:

y=a(x-4)²+k

Where (h, k) is the vertex of the parabola.

The vertex is (2, 4), and the parabola is stretched by a factor of 3. The negative sign in front of "a" indicates that the parabola opens downward.

So, we have:

Vertex: (h, k) = (2, 4)

Stretched factor:

a=-3

Now plug these values into the vertex form equation:

y=-3(x-2)²+4

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Answer:

(a): 10 civil servants who were absent.

(b): 15 civil servants are in field only.

Step-by-step explanation:

Let;

[tex]{ \rm{ \sum(n) = 90}} \\ \\ { \rm{n(o) = 65}} \\ \\ { \rm{n(f) = 50}} \\ \\ { \rm{(o \: { \huge{n}} \: f) = 35}}[/tex]

Question (a):

Let the absentees be x

[tex]{ \rm{x + (65 - 35) + (50 - 35) + 35 = 90}} \\ \\ { \rm{x + 80 = 90}} \\ \\ { \rm{x = 10}}[/tex]

There are 10 absentees.

Question (b):

Servants in field only;

[tex]{ \rm{n(f \: only) = 50 - 35}} \\ \\ { \rm{n(f \: only) = 15 \: servants}}[/tex]

Answer: they would earn $560

Step-by-step explanation:

10% = 400

1% = 40

0.1% = 4

40+16 = 56*10=560

If you could be so kind to press brainliest on this answer

Elliete's percentile rank is 96% for a score less than or equal to 246

The z score is used to determine by how many standard deviations the raw score is above or below the mean. The z score is given by:

[tex]z=\frac{x-\mu}{\sigma} \\\\where\ x=raw\ score,\mu=mean,\sigma=standard\ deviation[/tex]

Given that μ = 182, σ = 36

For x ≤ 246:

[tex]z=\frac{246-182}{36}=1.78[/tex]

From the normal distribution table:

P(x ≤ 246) = P(z < 1.78) = 0.9625 = 96%

Elliete's percentile rank is 96% for a score less than or equal to 246

Find out more on z score at: https://brainly.com/question/25638875